   Chapter 11.3, Problem 53E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 53 and 54, find the maximum and minimum values of y. Use a graphing utility to verify your conclusion. x 2 + y 2 − 9 = 0

To determine

To calculate: The maximum and minimum values of y if x2+y29=0.

Explanation

Given Information:

The provided equation is:

x2+y29=0

Formula used:

The power rule of derivative,

ddxxn=nxn1

The quotient rule of derivatives:

ddx[u(x)v(x)]=v(x)du(x)dxu(x)dv(x)dx[v(x)]2

Calculation:

Consider the provided equation:

x2+y29=0

Differentiate the both sides of the equation with respect to x as:

ddx(x2+y29)=ddx(0)

Now, apply the power rule of derivative:

2x+2yy=0

Solve for y as:

2x+2yy=02yy=2xy=xy

Now, the curve attains its maxima or minima where its derivative is zero

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